Preheat the oven to 350°F (175°C).
Grease a 7x10-inch bone-shaped silicone cake pan with 1 tablespoon of coconut oil.
In a large bowl, whisk together the oat flour, baking soda, and baking powder.
In a separate bowl, mash the ripe bananas using a fork. Add the eggs, melted coconut oil, peanut butter, and unsweetened oat milk. Mix well until combined.
Fold the wet ingredients into the dry ingredients, then gently stir in the grated carrot.
Pour the batter into the prepared cake pan and bake for 40-45 minutes, or until a toothpick inserted into the centre comes out clean.
Allow the cake to cool completely before removing it from the pan.
In a medium bowl, combine the Skyr or non-fat Greek yogurt and peanut butter. Use a hand mixer to whip the mixture until it's light and fluffy.
Spread the frosting evenly over the top of the cooled cake.
Optionally, you can decorate the cake with all-natural sprinkles for an extra special touch.